The Turán-Kubilius inequality for additive arithmetical semigroups |
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Authors: | S Wehmeier |
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Institution: | 1. Universit?t Paderborn, Warburger Str. 100, D-33098, Paderborn, Deutschland
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Abstract: | We show that the Turán-Kubilius inequality holds for additive arithmetical semigroups satisfying the following conditions:
G(n) = q
n
(A+O(1/ln n)) (where A > 0 and q > 1) for the number of elements of degree n and P(n) = O(q
n
/n) for the number of prime elements of degree n. This is an improvement of a result of Zhang. We also give some variants of the inequality under some stronger or weaker
assumptions and applications for the prime divisor function ω and related functions.
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Translated from Lietuvos Matematikos Rinkinys, Vol. 46, No. 3, pp. 457–471, July–September, 2006. |
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Keywords: | arithmetical semigroups Turán-Kubilius inequality |
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